On the cessation of seismicity at the base of the transition zone

Transcription

1 Journal of Seismology 2: 65 86, c 1998 Kluwer Academic Publishers. Printed in Belgium. On the cessation of seismicity at the base of the transition zone Emile A. Okal & Craig R. Bina Department of Geological Sciences, Northwestern University, Evanston, Illinois 60208, U.S.A. Received 8 July 1997; accepted in revised form 5 February 1998 Abstract Through a detailed analysis of seismicity at the base of the transition zone, we obtain an updated value of the maximum reliable depth of confirmed seismicity, we investigate regional variation in the maximum depth of seismicity among those Wadati-Benioff zones which reach the bottom of the transition zone, and we attempt to quantify the maximum possible rate of seismic release in the lower mantle compatible with the failure to detect even a single event since the advent of modern seismological networks. We classify deep subduction zones into three groups: those whose seismicity does not reach beyond 620 km, those whose seismicity appears to terminate around km, and Tonga-Kermadec (and the Vityaz cluster) whose seismicity extends to km. We suggest that the depth extent of seismicity is controlled by the depth of the! pv + mw transition responsible for the 660-km seismic discontinuity, which is deflected to greater depths in cold slabs than in warmer ones. We note that this transition marks the depth below which thermal perturbation of phase transitions no longer generates buoyancy anomalies and their large attendant down-dip compressive stresses and below which strain energy generated by other mechanisms may not accumulate to seismogenic levels due to superplastic weakness in fine-grained materials. We find that the maximum level of seismic activity in the lower mantle must be at least three orders of magnitude less than that observed in the transition zone. Introduction and background The purpose of this paper is to provide enhanced constraints on the cessation of seismicity around 690 km near the base of the transition zone. Our goal is severalfold: (i) to obtain an updated value of the maximum depth of reliably located global seismicity; (ii) to investigate the regional variation in the maximum depth of seismicity among those Benioff zones which do reach the bottom of the transition zone; and (iii) to attempt a quantification of the maximum possible rate of seismic release in the lower mantle which would be compatible with the failure to detect even a single event since the advent of the present seismological networks. We are motivated in this endeavor by the fact that any theory for the origin of deep earthquakes must in particular explain their cessation at the bottom of the transition zone. In this respect, it is important to give as precise a figure as possible for the maximum depth of confirmed seismicity, and to study its variation among slabs. In addition, recent tomographic models generally indicate that at least some slabs do penetrate into the lower mantle (e.g., Van der Hilst et al., 1991, 1997), thus refuting the earlier argument that earthquakes are absent from the lower mantle simply because subduction itself stops at the bottom of the transition zone. The unusual suggestion that earthquakes may actually occur in the lower mantle deserves some discussion. The idea of a global limit to the depth-extent of deep seismicity may, for example, be compared to apparent regional limits on the depth-extent of seismicity. In many areas of the world, seismicity stops at intermediate depths, even though we know from tomographic studies that the slab actually penetrates deeper than the maximum extent of seismicity. However, in several instances, a number of isolated, rare earthquakes have been documented beyond doubt at depths greater than the generally recognized limit of seismic activity in the relevant subduction zone. The most striking example is New Zealand where Adams (1963) and Adams and Ferris (1976) have identified the repeated occurrence of small events around 585 km depth, more than 270 km below the rest of the Wadati- Benioff Zone (hereafter WBZ), with a few more such

2 66 earthquakes taking place since the early 1990s. Similarly, in the South Sandwich Islands, two earthquakes occurred at the Northern (01 Jan 1979) and Southern (05 Oct 1997) ends of the arc, more than 100 km deeper than their closest neighbors. Thus, we must accept that exceptions to the general patterns of seismicity with depth in individual seismic zones are undeniable. Note that some of the very largest deep earthquakes (such as the Colombian earthquake of 1970, the Peruvian earthquakes of (Okal and Bina, 1994), or the Spanish earthquake of 1954 (Chung and Kanamori, 1976)) have occurred as isolated events taking place several hundred km below the apparent termination of the WBZ. The occurrence of such situations raises the possibility that the observed aseismicity of the deep mantle may be an artifact of poor detection capabilities (both in terms of a magnitude threshold for detection at the surface and of a relatively short period of observation at an adequate detection level) and that an earthquake may one day be observed in the deep mantle. There is no compelling reason why the thermal regime of the slab should prohibit seismicity below depths of 690 km. The temperatures of the slab should not rise significantly at this depth; indeed, the endothermic nature of the transition from to pv + mw should actually coolthe slab in this depth range. With regard to mineralogical regime, certain proposed mechanisms for initiation of deep seismicity, such as transformational faulting or adiabatic instability, require the occurrence of kinetically delayed exothermic phase transitions, and these are much less likely to occur in lower mantle pv + mw mineral assemblages than in shallower + gt assemblages. However, there is no obvious mechanical or rheological reason why all potential mechanisms for seismic stress release should cease to operate in the lower mantle. On the other hand, if the lower mantle truly is aseismic, this may reflect a general absence of large deviatoric stresses below 690 km, rather than the absence of mechanisms for seismic stress release. The depth of the deepest earthquakes: an update In view of the abrupt cessation of seismicity at or around 700 km depth, a number of studies have addressed the question of the precise value of the maximum recorded depth of earthquakes. Among recent works, Stark and Frohlich (1985) have examined about 100 very deep events from the catalogue of the International Seismological Centre (ISC) covering the years and concluded that none could be reliably located below 685 km on the basis of pp P readings. In addition, Rees and Okal (1987) have used International Seismological Summary (ISS) listings of historical earthquakes ( ) whose original location was 670 km or deeper, and relocated 23 such events to depths less than or equal to 691 km. The precision of their relocations (estimated at 10 km) put their results in total agreement with Stark and Frohlich s (1985). However, they were unable to constrain the depth of 10 events, eight of which were not listed in the ISS. Our purpose here is to update these studies in several ways: (i) to investigate the post-1980 events which were listed by the National Earthquake Information Center (NEIC) at depths greater than 690 km; (ii) to complete the work of Rees and Okal (1987) by including data from the Bureau Central International de Séismologie (BCIS) compiled at Strasbourg, and not available to Rees and Okal; and (iii) to examine critically the depth of the deepest earthquakes in individual deep slabs to identify any regional variation in this parameter. We use the relocation method described in detail by Wysession et al. (1991), which is based on an interactive iterative least-squares algorithm; it also uses a Monte Carlo approach to systematically inject Gaussian noise (with standard deviation G ) into the data to study directly the level of resolution of the various variables (most critically depth in the present application). We use G = 1 s for modern events, but larger values for historical ones. Since the study of Stark and Frohlich (1985), eight events (all in the Fiji Tonga subduction zone) have been assigned depths greater than 690 km by the NEIC. These are listed in Table 1 and discussed individually in the Appendix. Among them, five relocate between 562 and 685 km. Two more relocate at 709 and 710 km respectively, but with such poor depth resolution that hypocentral depths of 690 km are just as acceptable. The last event (19 May 1992) moves to 282 km when carefully relocated, as indicated by the ISC solution. Among the historical events studied by Rees and Okal (1987), 10 earthquakes could not be relocated, for lack of adequate data. Having recently acquired a complete microfiche copy of the Bulletin of the BCIS, we were able to relocate eight of these earthquakes at depths ranging from 61 to 685 km. Among the remaining two, the event on 10 October 1957 relocates at 712 km, but with poor depth control, so that a solution at 690 km is just as acceptable. The dataset for the final event (14 July 1959) provides minimal depth resolution; this is a small aftershock of an event which

3 67 Table 1. Events postdating Stark and Frohlich s (1985) dataset with NEIC depths greater than 690 km Date and Origin NEIC hypocenter ISC hypocenter Relocated hypocenter (this study) Magnitude Time D M Y GMT Latit. Longit. Depth Latit. Longit. Depth Latit. Longit. Depth Numb. of m b N E (km) N E (km) N E (km)y stations (s) : F : F : C : C : F : C : F : F y: F: Floating depth relocation; C: Monte Carlo relocations indicate no depth control; solution obtained with constrained depth. relocates at 627 km, however, and the solution for the aftershock with the depth constrained at this value yields excellent residuals ( = 0:53 s). Details on all these relocations are listed in the Appendix. In conclusion, newly acquired data (in the form either of new events which occurred after the time window available to Stark and Frohlich (1985) or of BCIS bulletins complementing the dataset used by Rees and Okal (1987)) fully uphold the conclusions of these two studies: there are no earthquakes reliably located at depths greater than 690 km, with a precision estimated at 10 km. Regional variation in the depth of the deepest earthquakes In this section, we consider the regional variation of the maximum depth of earthquakes in those slabs whose seismicity does reach into the deepest part of the transition zone, namely below 620 km. Our goal in this work is to examine to what extent this maximum depth varies between slabs and which parameters may control any such variation. We refer to the previous works by Kostoglodov (1989) and Kirby et al. (1991, 1996), who introduced the notion of the thermal parameter,, computed as the product of the age of the material in the slab and its vertical descent rate. These authors have observed that subduction zones for which km do not exhibit deep earthquakes, while those with > km feature seismicity throughout the transition zone. We seek to refine the latter statement, specifically to determine if a further trend can be robustly identified on a small scale between thermal parameter and maximum depth among the deepest populations analyzed on Kostoglodov s (1989) Figure 2 or Kirby et al. s Figures 9 (1991) or 4 (1996). Specifically, we investigate whether any trend exists in the maximum depth of seismicity between slabs with thermal parameters barely over km (e.g., Java), those approaching km (e.g., Marianas), and Tonga, whose may be as large as km. Following Marton et al. (1997), however, we caution that the definition of the thermal parameter may be inadequate in the case of the subduction of very old lithosphere, for which the thickness of the plate (which controls the rate of diffusion of heat into the cold slab) has tapered off to around 100 km (Parsons and Sclater, 1977; Stein and Stein, 1992) and is no longer a strong function of the age of the lithospheric material. Since we are concerned only with the mechanism by which seismicity stops at the bottom of the transition zone, we do not consider here those slabs whose seismicity ceases above 600 km depth, and we thus restrict ourselves to the following subduction zones: Tonga- Kermadec, Solomon, Sangihe (Southern Philippines), Marianas, Java (West of 115 ), East Sunda (East of 115, including Banda Sea), Kuriles, Peru, Bolivia, and Argentina, as well as isolated events in Colombia and Northern Peru, Spain, and the detached Vityaz slab under the North Fiji Basin. Note that with the exception of Solomon and Sangihe, where the tectonic regime is extremely complex and possibly transient, all the above slabs involve the subduction of old plates, i.e., lithosphere having attained its maximum thickness beyond the age of 90 m.y. In terms of thermal properties, the main difference between these various zones

4 68 Table 2. Reassessment of historical events not relocated by Rees and Okal (1987) Date and Origin NEIC hypocenter BCIS(*) hypocenter Relocated hypocenter (this study) Remarks; Time D M Y GMT Latit. Longit. Depth Latit. Longit. Depth Latit. Longit. Depth Numb. of Action N E (km) N E (km) N E (km) stations (s) taken : I F Increase Amboina by 1 mn; no depth control : No location F Poor depth control : F Typographic error : F Typographic error : F Increased P at BRS by 1 mn; Decreased S atmatby1mn : F Use BCIS data : C Use BCIS data : C Constrain depth to same as main shock : F Use BCIS data; eliminate RIV, SHL : discordant data F Increase CAN and CTAby1mn; eliminate BHA y: F: Floating depth relocation; C: Monte Carlo relocations indicate no depth control. Solution obtained with constrained depth. ( ): I: ISS solution when no BCIS one is available. will arise from their rate of subduction, not from the absolute age of the material being subducted. In the subsequent paragraphs, we investigate the maximum depth of seismicity in each of these subduction zones, based on the following datasets: the computerized NEIC dataset; ISC inverted hypocenters, generally available after 1963 (most often with a precision estimate); ISC hypocenters estimated from pp P (generally available for larger events); centroid depths from the inversion of moment tensors (Dziewonski et al., 1983, and subsequent quarterly updates for events postdating 1976, available for M dyn-cm; Huang et al., 1997 for WWSSN solutions, available for M dyn-cm); depths inverted by Engdahl et al. (1997), available for larger events and during In the case of smaller events for which few depth estimates were available, we conducted our own relocations (including Monte Carlo tests) based on ISC or BCIS listings. We also include results from a few historical events, when the latter are significant or their discussion relevant. All data are listed in Table 3. Preliminary results of the present study were included in

5 69 Table 3. Deepest events in Deep Wadati-Benioff Zones ( ) Date Magnitude Depth (km) Remarks D M Y [hh:mm] m b NEIC ISS/ISC ISS/ISC CMT This Monte EHB (Inverted) pp (y) Study Carlo (y) Java [10 S 3 S; 105 E 115 E] D H D D Conclusion: Seismicity stops around 660 km East Sunda including Banda Sea [10 S 3 S; 115 E 130 E] D D D Deepest CMT solution (6: ) Rees and Okal (1987): 691 km Conclusion: Seismicity stops around 660 km Solomon Islands [8 S 3 S; 150 E 160 E] Only event below 620 km Conclusion: Seismicity stops around 605 km Sangihe South Philippines [2 N 10 N; E] Deepest NEIC-reported D 658 Deepest large event Conclusion: Seismicity stops around 660 km Mariana Islands [10 N 20 N; 140 E 150 E] H Stark and Frohlich: km Conclusion: Seismicity stops around 660 km

6 70 Table 3. (continued) Date Magnitude Depth (km) Remarks D M Y [hh:mm] m b NEIC ISS/ISC ISS/ISC CMT This Monte EHB (Inverted) pp (y) Study Carlo (y) Kuriles Kamchatka [42 N 55 N; 140 E 160 E] D H D 641 Conclusion: Seismicity stops around 650 km Argentina [30 S 13 S; 66 W 55 W] H 600 Conclusion: Seismicity stops around 620 km Bolivia [15 S 12 S; 71 W 66 W] : : D : aftershocks located by Myers et al. (1995) from 622 to 660 km, plus one at 665 km Conclusion: Seismicity stops around 660 km Peru Brazil [12 S 7 S; 73 W 70 W] H D H Significant historical event Conclusion: Seismicity stops around 650 km Tonga [35 S 15 S; 175 E 175 W] : All-time deepest ISC solution : Second-deepest ISC solution Deepest NEICreported; no depth control See Table : See Table See Table : See Table See Table

7 71 Table 3. (continued) Date Magnitude Depth (km) Remarks D M Y [hh:mm] m b NEIC ISS/ISC ISS/ISC CMT This Monte EHB (Inverted) pp (y) Study Carlo (y) Tonga (continued) Deepest event in Engdahl et al See Table See Table See Table D : D 676 Conclusion: Seismicity reaches 690 km Northern Peru Colombia [5 S 1 S; 75 W 70 W] GR (Okal and Bina, 1994) GR H 660 (Okal and Bina, 1994) R Conclusion: Seismicity stops around 660 km Spain [35 N 40 N; 5 W 0 W] Rupture propagated 20 km downwards (Chung and Kanamori, 1976) Conclusion: Seismicity stops around 650 km Vityaz Cluster [16 S 11 S; 167 E 177 E] : : : : :

8 72 Table 3. (continued) Date Magnitude Depth (km) Remarks D M Y [hh:mm] m b NEIC ISS/ISC ISS/ISC CMT This Monte EHB (Inverted) pp (y) Study Carlo (y) Vityaz Cluster (continued) D : : Conclusion: Seismicity stops around 672 km Other event (Japan Sea) No depth resolution NEIC probably erroneous y D: Harvard CMT (Dziewonski et al., 1983 and subsequent quarterly updates); H: Huang et al. [1997]; R: Russakoff et al. (1997). EHB: Engdahl et al. (1997). the review of deep seismicity by Kirby et al. (1996). The precision sought in these descriptions is never better than 10 km. Table 3 shows that there exists a systematic, but not universal, trend for Engdahl et al. s (1997) relocations to be shallower than the ISC and NEIC solutions and than our own relocations. As discussed in greater detail by Van der Hilst and Engdahl (1992) and Engdahl et al. (1997), this reflects a combination of the use of Kennett et al. s (1995) model ak135 as opposed to Jeffreys and Bullen s (1940) Tables, the non-random distribution of stations, and the use of use of depth phases (mostly pp ) by Engdahl et al. (1997), which compensates to some extent the bias introduced by propagation of a significant fraction of rays through fast material in subducting slabs.at any rate, the magnitude of this trend is less than the precision sought in the present study. We also take this opportunity to emphasize that there remains a small level of potential incompleteness in the various tables we present. Our procedure does not guard against the possibility that an event listed as shallow by all cataloguing agencies (NEIC, ISC, etc.) could actually be among the deepest in a subduction zone. The only perfectly foolproof approach to this problem would be to re-examine every single earthquake of any depth recorded since the beginning of reliable bulletins (ca. 1920). This herculean task is clearly beyond the scope of the present study, but some perspective can be found in Engdahl et al. s (1997) relocation catalogue: out of a total of entries, these authors list only 11 earthquakes with shallow catalogue foci (constrained at 0 or 33 km in all cases) which they relocated in the transition zone (h 400 km), none of them at the tip of the WBZ. Java The combination of precise ISC locations and CMT inversions suggests that seismicity stops around 660 km, although Engdahl et al. s (1997) relocations would place the deepest earthquakes about 10 km shallower. East Sunda Arc including Banda Sea The combination of precise ISC locations, CMT inversions and our own relocations places the deepest earthquakes around 660 km, although again, Engdahl et al. s hypocenters are 15 km shallower. The only exceptions are the 1963 NEIC listing, for which our study suggests very poor depth resolution. The figure of 660 km is also in general agreement with the results of Rees and Okal (1987), who studied seven historical earthquakes in this area. Only their solution for 11 May 1955 was significantly deeper (691 km), but Monte Carlo tests show very poor depth resolution for this event.

9 73 Solomon Islands Because there is only one Solomon Islands hypocenter listed below 620 km by the NEIC (22 April 1991, 626 km; m b = 4:8), we include in Table 3 all earthquakes below 590 km in this region. The 1991 earthquake is listed by the ISC at an equivalent depth (627 km); however, our Monte Carlo relocations on the available dataset of only 10 stations range from 589 to 656 km, indicating mediocre depth control. Seismicity is otherwise documented robustly in the 600 to 610 km range, and there is no reason to believe that the 1991 earthquake is any deeper. The maximum depth of seismicity in the Solomon Islands is taken as 605 km. Sangihe South Philippines All available information indicates that seismicity ceases around 660 km, including well constrained ISC locations (25 Apr 1969; 05 Mar 1984), Engdahl et al. s (1997) relocations (05 Mar 1984), and our own Monte Carlo tests (25 Apr 1969; 25 Jan 1993). This figure is also in agreement with the work of Rees and Okal (1987), who found a maximum depth of 662 km for the Mindanao earthquake of 22 Sep Mariana Islands The case of the Mariana WBZ is somewhat singular in that the deepest reported event (07 Mar 1962, 685 km (NEIC)) is also one of the largest in that slab below 500 km. While the NEIC and ISC report it as very deep, both our relocations and Stark and Frohlich s (1985) suggest a somewhat shallower depth around 670 km. Furthermore, a relocation constrained at the inverted centroid (661 km, Huang et al. (1997)) is not significantly deteriorated with respect to our best hypocenter ( = 1:43 s as opposed to 1.40).We therefore adopt the figure of 665 km for the maximum depth of seismicity in the Marianas, while remembering that it reflects the average of various estimates for a single earthquake. Kuriles Kamchatka The various datasets are very consistent, notably regarding the great 1970 deep shock, and suggest a maximum depth of 650 km for this WBZ. Argentina Since 1962, only 4 earthquakes were reported at or below 620 km by the NEIC. Of those, the small 1968 earthquake (641 km) has very poor depth resolution, but is most probably much shallower, and the large 1962 earthquake is most certainly no deeper than km. The reasonably robust event in 1984 suggests 620 km as the maximum depth of seismicity under Argentina. Bolivia The case of this segment of the South American subduction zone is special, since its seismicity consists nearly exclusively of the great 1994 event and its aftershocks. The extensive study by Myers et al. (1995) indicates a maximum depth of 660 km (except for a lone event at 665 km, for which no estimate of precision is given). Peru Brazil Precise NEIC and ISC relocations suggest 650 km as a maximum depth, although the other sources would argue for a figure 10 km shallower. The dataset for the small 1987 event has poor resolution, and its greater depth is not robust. The centroid for the large 1950 shock (649 8 km) also supports a maximum depth of 650 km, as do the results of Rees and Okal (1987) on the shocks of 26 Nov 1945 (640 km), 18 Sep 1950 (647 km) and 28 Dec 1950 (657 km). Tonga Kermadec As detailed in numerous studies (Giardini, 1984; Stark and Frohlich, 1985; Rees and Okal, 1987; Engdahl et al., 1997), there is ample evidence that seismicity reaches 685 km, and a few earthquakes are well documented at 690 km in the Tonga Kermadec subduction zone, these figures having an uncertainty of about 5 km (e.g., 25 Sep 1971, 22 Oct 1985 (19:13)). We refer to Table 1 and the discussion in the previous section regarding post-1980 events reported deeper than this figure. We also examined in detail a few earthquakes described by Stark and Frohlich (1985) with reported depths greater than 690 km. The most puzzling cases are the two ISC reports for 07 May 1971 at 22:30 (848 km) and 25 Oct 1972 (806 km). Neither shock is reported by the NEIC; however, our relocations move

10 74 these events to hypocenters at 624 and 433 km, respectively, with Monte Carlo depths reasonably constrained to the intervals km and km. Also, the 1971 earthquake appears to be an aftershock of a previous shock, occurring three hours earlier, given by the NEIC at 606 km, by the ISC at 664 km, and which we relocate at 575 km. We are at a loss to figure out the origin of those exceedingly deep ISC solutions, in view of the existence of much shallower satisfactory solutions. The nearly coeval character of these two instances, and the fact that they did not recur in the next 22 years, as well as the unrealistic error bars in the ISC solutions, would suggest a change of algorithm in the ISC computation, with the application of more stringent quality control some time after The situation with the deepest NEIC solution (31 Oct 1977) is somewhat different in that all inversions locate it around 730 km, but the solution has absolutely no depth resolution, as indicated by our Monte Carlo tests (the maximum Monte Carlo depth is artificially constrained at 800 km in our program). Thus, we confirm that the exceedingly deep foci reported by the NEIC and ISC are artifacts of datasets with poor resolution, unstable location algorithms or both. Isolated shocks: Northern Peru and Colombia; Spain In these two regions, a few, rare, isolated earthquakes are documented at the bottom of slabs which are otherwise inactive below 300 and 150 km, respectively. Because of the rarity of these events, we cannot regard their hypocenters as marking precisely the depth of maximum seismicity in the relevant regions. However, it is interesting to note that in both instances these shocks seem to take place in (or their source regions to extend to) the immediate vicinity of the maximum depth of activity commonly identified in many other subduction zones (650 to 660 km). Specifically, in Northern Peru and Colombia, only three large shocks are known; the depth of the 1970 earthquake is constrained to within a few km of 650 km; as for the 1921 and 1922 events, Okal and Bina (1994) have proposed depths of 630 and 660 km, respectively. In Spain, only three small events have been detected in the vicinity of the 1954 large deep earthquake. The latter s hypocenter is very well constrained to 6303km, with a downward rupture extending to 649 km (Chung and Kanamori, 1976). As for the smaller events, their depths are comparable. The Vityaz cluster This group of earthquakes, located deep under the North Fiji Basin, has recently been investigated by Kirby and Okal (1996), who interpret them as occurring in the remnant of a so-called Vityaz slab, lying recumbent at the bottom of the transition zone. The slab subducted southwestwards under the Australian plate until 8 million years ago, when it was deactivated as part of the reorganization of the plate boundary system in the region (Chase, 1971; Hamburger and Isacks, 1987). As detailed in Table 3, well constrained ISC and NEIC solutions are found regularly at a maximum depth of about 665 km, with one well constrained event at 672 km (01 Dec 1981, 14:18) and two more at 674 (12 Aug 1979) and 677 km (01 Dec 1984, 14:13); note however that Engdahl et al. (1997) would place these events about 20 km shallower. As for those events located deeper (down to 683 km) by Okal and Kirby (1996), they have much poorer depth resolution, as indicated by our Monte Carlo tests. We use 672 km as the maximum depth of seismicity in the Vityaz cluster. Other event Finally, the NEIC tape lists one event below 620 km belonging to neither of the above slabs, namely under the Sea of Japan on 16 Dec 1977 (33:0 N, 136:4 E, 637 km). The ISC lists it at 380 km, and our relocation converges on 543 km; however, the dataset has little depth resolution, and the earthquake can be accommodated between 330 and 410 km, the range of robust solutions in that part of the Honshu slab. Discussion The pattern emerging from the above study is that of relatively discontinuous behavior of the depth of maximum seismicity among those WBZs reaching the deepest parts of the transition zone. These can be classified into three groups. Group (i) consists of those subduction zones whose seismicity does not reach beyond 620 km: Solomon, Argentina. Group (ii) contains a large set of deep subduction zones for which there is documented seismicity below 620 km and whose WBZs all seem to terminate around km: Sangihe, Banda Sea, Java, Kuriles, Bolivia, Peru- Brazil. The maximum depth in the Marianas, 665 km, is not significantly greater than this figure, and the isolated seismicity in Colombia-Northern Peru and Spain also fits this general pattern. Note that this set

11 75 Figure 1. Deepest seismicity in deep-reaching subduction zones, as compiled from the data in Table 3, as a function of their subduction thermal parameter,. The latter are taken mainly from Kirby et al. (1991), with parameters for the Tonga and the South American segments adjusted in the light of new data (Bevis et al., 1995) or models (Engebretson and Kirby, 1992). Sangihe and Solomon trenches not included for lack of precise kinematic model, nor are the detached Vityaz slabs and the isolated events of Spain and Colombia. regroups subduction zones with thermal parameters varying between and km as documented in Kirby et al. (1996). In other words, and as illustrated on Figure 1, there is no apparent influence of on the maximum depth of seismicity for this group. Group (iii) consists of the Tonga Kermadec subduction zone, whose seismicity extends down to km, as well as the seismicity of the deep, probably recumbent Vityaz cluster below the Northern Fiji Basin (maximum depth 672 km). These observations strongly suggest that, within a well developed, mature subduction zone, the depth extent of seismicity is controlled by the depth of the second mantle discontinuity. The latter should be about 660 km in undisturbed mantle; due to its negative Clapeyron slope (Navrotsky, 1980), the equilibrium! pv + mw transition is deflected to greater depths within the thermal fields of colder slabs than in those of warmer slabs. If, following Kirby et al. (1996), we adopt 300 K as a representative temperature difference, at 660 km depth, between a slow, relatively young slab (such as Java), which will be warm (if not hot ) among the slabs whose seismicity reaches the bottom of the transition zone, and a very fast, very old and therefore very cold one (such as Tonga), and if we assume an effective Clapeyron slope of 3 1MPa/K for the! pv + mw transition (Bina and Helffrich, 1994), we find that the transition in the cold slab will be deflected by an additional MPa in pressure, or 279 km in depth, relative to the transition in the warm slab (Figure 2). This is in remarkable agreement with our observation that deep seismicity in the Tonga subduction zone extends km below that in other, warmer subduction zones. The case of the only other zone of seismicity consistently deeper than 660 km, the Vityaz cluster, is more complex. The most probable model for its origin leaves little doubt that the material is composed of very old lithosphere, having come from the long-defunct Phoenix Ridge (Engebretson et al., 1991), but we can only speculate on its velocity of subduction. The mechanical separation of the recumbent piece of slab from the Pacific plate s lithosphere may have resulted in much faster sinking (at least initially), which could conceivably leave the seismogenic material significantly colder than the adjoining mantle. Meanwhile, in all other subduction zones, the downward deflection of the discontinuity would remain less than 15 km and thus probably within the uncertainty of our estimates of maximum depth. In the previous section, we have presented phenomenological evidence suggesting that the depth of maximum seismicity appears to be controlled by the depth of the second mantle transition in individual subduction zones. In attempting to explain why this might be so, three possible explanations are immediately evident: (1) an appropriate mechanism of seismic release (e.g., transformational faulting,dehydration, partial melting) cannot operate at greater depths, (2) material strengths below these depths are too low to permit the accumulation of strain energy to potentially seismogenic levels, or (3) there are no large stresses generated beyond these depths which would engender seismic release. With regard to seismic release (1), while certain proposed mechanisms (e.g., transformational faulting, adiabatic instability) require the occurrence of kinetically retarded exothermic phase transitions which are unlikely to occur in the lower mantle, we know of no compelling reason that all potential mechanisms of seismic stress release should suddenly cease to be viable below the depth of the! pv + mw transition. However, given the uncertainty surrounding the operative mechanisms of seismic release even at shallower depths, we cannot rule out this possibility. With regard to strain accumulation (2), while olivine grows progressively less able to store strain energy for seismogenesis with increasing temperatures

12 76 Warm Slab Cool Slab pv+mw Depth (km) γ 8.5 γ+pv+mw Depth (km) Buoyancy (kn/m 3 ) Depth (km) σ max (MPa) x (km) x (km) -54 [Okal & Bina, 1997] Figure 2. Equilibrium depth of the! pv + mw transition (top), corresponding buoyancy anomalies (middle), and consequent (absolute) maximum principal stresses (bottom; negative = compression) for warm (left) and cold (right) slabs. The 1500 K isotherm is labeled and adjoining ones at 300 K intervals shown. Vertical exaggeration is 4:1. due to its declining strength, transition zone minerals such as the and phases are significantly stronger than olivine (Weidner, 1997). However, the pv + mw assemblage produced below the 660-km discontinuity should be fine-grained, possibly producing a weak superplastic zone which is incapable of storing seismogenic elastic energy (Ito and Sato, 1991), a hypothesis which is consistent with the absence of observed seismic anisotropy in the lower mantle (Karato, 1998). Moreover, while any potentially seismogenic adiabatic instabilities occurring at moderate slab temperatures would be promoted by the high strain rates induced by such grain-size reduction, such instabilities would be terminated by negative latent-heat release at the 660- km transition (Karato, 1997). Thus, it is plausible that strain energy may accumulate less efficiently below the! pv + mw transition.

13 77 With regard to stress generation (3), a case can be made as to why there should be no large stresses to be released seismically at depths below the! pv +mw transition. The cold thermal field of the slab acts to deflect the equilibrium depths of the!! transitions upwards while (Figure 2) deflecting the deeper! pv + mw transition downwards (Schubert et al., 1975). The attendant buoyancy anomalies result in large down-dip compressive stresses in the region between these phase transitions, which are reflected in the distribution and mechanisms of deep earthquakes (Ito and Sato, 1992; Bina, 1996). Below the! pv + mw transition, however, there is no such mechanism for generating large compressive stresses through opposed buoyancy anomalies, and the slab reverts to small tensional stresses (Bina, 1997). These tensional stresses fall off rapidly with depth because the negative thermal buoyancy of the slab decreases as the slab thermally equilibrates with increasing depth of penetration, and they are of significant magnitude only immediately below the! pv + mw transition. No down-dip tensional seismicity is known from this region, and any slab bending (Lundgren and Giardini, 1992; Van der Hilst, 1995) in response to the buoyancy forces or any encounter with putative viscosity increases (King, 1995) would counteract these tensional stresses. (The region of large compressive stress outside the thermal halo of the slab in Figure 2 arises from gravitational loading of the inclined slab on the underlying mantle material and occurs where the mantle is too warm to support seismicity.) Thus, as the equilibrium depth of the! pv + mw transition increases (linearly) in colder slabs, the depth to the corresponding cutoff in down-dip compressive stress also increases (nonlinearly). In summary, the! pv + mw transition occurs at a greater equilibrium depth in colder than in warmer slabs, and this transition marks the depth below which buoyancy anomalies no longer generate the large down-dip compressive stresses associated with seismicity. Furthermore, any stresses generated by other mechanisms may be unable to accumulate seismogenic levels of strain energy below this transition, due to the probable formation of a fine-grained, weak, superplastic zone in the pv + mw stability field. Thus, the depth of cessation of seismicity should be greater for colder slabs than for warmer ones, just as we observe. Quantifying the maximum possible moment release in the deep mantle Just how aseismic is the deep mantle? We have yet to confidently locate a single earthquake below 690 km depth, but one cannot exclude the possibility that some seismicity could be present at greater depths, either at low magnitudes escaping detection at the surface or taking place too infrequently to have been observed since the inception of the world-wide seismograph network in the early 1960s. In this section, and based on a few hypotheses on detection thresholds and frequencysize relations, we derive an estimate of the maximum possible level of moment release rate of such undetected events in the deep mantle, below the transition zone. For the purpose of comparison with seismicity in the transition zone, we will use as a reference period the time window which, as of the date of writing, constitutes the latest full-year span of the Harvard centroid moment tensor solutions (Dziewonski et al., 1983, and subsequent quarterly updates). The threshold of completeness for the observed aseismicity of the deep mantle We must first assess the moment threshold above which we can confidently claim that no earthquake has occurred in the deep mantle during the reference period. Detection capabilities are directly related to the amplitude of body waves excited by a source with a given seismic moment. In turn, this is controlled by several terms (e.g., Okal, 1992), primarily the far-field P -wave excitation coefficient 1= 3 and the geometrical spreading factor g(;h). We have verified that at a given distance, these terms will be only very slightly affected when sinking the source below the 670-km discontinuity: the change of amplitude for a P -wave would correspond to less than 0.1 unit of magnitude (Okal, 1993). As a result, detection capabilities are expected to be similar at the bottom of the transition zone and in the lower mantle, taken here as the depth range 690 < h 1000 km. In the case of the very deepest transition zone earthquakes ( km), Okal and Kirby (1995, Figure 5) have shown that the frequency-size relationship is linear down to dyn-cm, suggesting that the dataset is complete down to that value, and we can therefore state confidently that no earthquake of moment M dyncm located in the lower mantle would have escaped detection during the CMT era. We will use this value

14 78 (10 24 dyn-cm) for M thresh, the threshold of completeness for the aseismicity of the deep mantle. Modeling the frequency-size distribution of possible seismic events in the lower mantle It is obviously very difficult to propose a model for a population of which no member has ever been observed. In this endeavor, we assume that potentially seismogenic material in the deep mantle would take the form of blobs, whose fractal dimension can be taken as 3 (as in the transition zone), as opposed to 2 in the case of shallow earthquakes distributed on faults. We further assume that deep-mantle earthquakes would involve shear faulting on a planar surface, so that the familiar relation M 0 = S u would hold, and that the physical saturation of earthquake source dimensions would involve the same regimes as for transition zone shocks. In other words, we make here the uniformitarian assumption that the properties of seismic events in the lower mantle would be comparable to those in the transition zone, as studied by Okal and Kirby (1995). Under these conditions, we consider a population of deep mantle earthquakes with a frequency-moment distribution following a three-tier law of the form log 10 N = a 1 1 log 10 M 0 for M 0 M 1 log 10 N = a 2 2 log 10 M 0 for M 2 M 0 M 1 (1) log 10 N = a 3 3 log 10 M 0 for M 0 M 2 : By comparison with transition zone earthquakes, and based on fractal dimensionality arguments, we take 1 = 3 = 1; 2 = 1=2. Then, in order to ensure continuity at the corner moments M 1 and M 2, a 1 = a log M ; a 2 = a 3 M 2 2 log 10 M 2 (2) where the constants a i would depend on the particular reference time window. The total seismic moment release in a moment window fm min ; M max g spanning the three regimes is simply given by M 0=M Z max [M 0 ] max min = M 0=M min M 0 ( dn ) = 10 a3 ln M 2 M min + 10 a2 p M1 p M2 +10 a1 ln M max M 1 (3) Over the length of the reference period, = 19 years, the total rate of seismic moment release is simply Rmin max = 1 [M 0] max min. For 1 = 1, the moment integral diverges as M max!1, which simply means that there is some dimension (if nothing else, the Earth s radius) controlling the maximum size of an earthquake. More realistically, we will use as M max the moment of the largest deep earthquake ever recorded, 2: dyn-cm. Similarly, for 3 = 1, the moment integral diverges as M min! 0, which simply expresses that the scaling laws will not be valid below some minimum dimension of the source (if nothing else, the grain size of the material). More realistically, Rundle (1993) has shown that in the case of shallow earthquakes, the existence of a region with inelastic properties (fault gouge) introduces a length scale c in the problem, and results in a Fermi-Dirac frequency-size distribution, which coincides with the Gutenberg-Richter relation only when the characteristic size L of the event is much larger than c. This behavior ensures the convergence of the moment integral. Rundle estimated c to be on the order of a few tens of meters for shallow events, corresponding to a critical moment M c = 1: dyn-cm. As detailed below, we will assume that a similar limitation exists for transition zone or deeper earthquakes, even though the nature of the characteristic length c may remain unclear. For practical purposes, we will first compute the seismic moment integral over the interval fm thresh ; M max g, and then adjust it to include the contribution of smaller earthquakes obeying the Fermi-Dirac distribution. We assume that the detection threshold M thresh falls below the critical moment M 2 ; then, the rate of seismic moment release in the relevant interval is given by: Rthresh max 1 r = [M 0] max thresh = 10a3 M1 ln M max + 1 M 1 M 2 M 2 + ln M 2 1 (4) M thresh That no earthquake has been located in the deep mantle, above the detection threshold M thresh, simply means that N (M thresh ) < 1ora 3 < 3 log 10 M thresh.inturn this leads to: Rthresh max < M r thresh M1 ln M max + 1 M 1 + ln M 2 1 (5) M thresh Of course, the seismic moment actually released in the deep mantle during the CMT era beyond M thresh is

15 exactly zero. In this respect, Rthresh max simply represents the maximum rate of seismic moment release which would be expected to remain undetected during an average 19-yr period, since it would produce less than 1 earthquake in the moment window fm thresh ; M max g during that time. We have no control over possible values of M 1 and M 2 in (1). These quantities would be related to the size of the seismogenic blobs, and they can only be the subject of speculation. In the following discussions, we will first assign to the lower mantle values adequate for the deepest part of the transition zone (M 1 = and M 2 = dyn-cm; (Okal and Kirby, 1995)). We will refer to this model as the extrapolated estimate, which should provide an order of magnitude of the seismicity expected in the context of a uniformitarian model attempting to maximize the similarity between the two domains under study. On the other hand, we will also study [M 0 ] max thresh as a function of M 1 and M 2, with the simple restrictions M 2 M thresh and M 1 M max. We will call the bounds on the resulting values of (5) the estimated range of rate of moment release. Figure 3 shows that under these conditions, the extrapolated rate for Rthresh max Mthresh is 43 times (or 2: dyn-cm/yr) with the estimated range varying from 10 to 195 times Mthresh, or from 5: to 1: dyn-cm/yr, for the period These numbers can be compared to the total rate of seismic moment release during the same time window for earthquakes taking place in the transition zone (400 to 690 km). In that depth range, the total seismic moment release from the CMT catalogue is 4: dyn-cm, corresponding to a rate of 2: dyncm/yr, 1130 times more than the extrapolated estimate, and 260 to 4900 times the bounds of the estimated range. Estimating the contributions below M thresh However, these numbers relate only to that part of the moment released above the detection threshold M thresh. It is possible to extend the comparison by including the contribution of earthquakes at smaller magnitudes. For this purpose, we assume that the events follow a Fermi-Dirac distribution, modified from Rundle s (1993) Equation (26) to reflect the different fractal dimension of the source: N = 10 (A 1:5mc) log :5(mc m) (6) which can be rewritten as a function of moment M 0, rather than magnitude, as: 79 N = 10 (A 3a=2) Mc 1 log M c M 0 (7) where it has been assumed, following Rundle (1993), that the magnitude m is related to seismic moment through: m = 2 3 log 10 M 0 + a (a = 10:73) (8) and the corner moment M c is obtained by substituting m = m c in (8). For large moments, this distribution is equivalent to log 10 N = z log 10 M 0 with z = A 3 2 a + log 10 (log 10 e)=a+15:73: (9) The total seismic moment released between M 0 = 0 and M 0 = M thresh is then [M 0 ] thresh 0 = Z M 0=M thresh M 0=0 M 0 ( dn ) = 10 z ln 1 + M thresh : (10) M c When applying this result to the deep mantle population, we just replace z by a 3 and obtain a contribution [M 0 ] thresh 0 = 10 a3 ln 1 + M thresh M c M thresh ln 1 + M thresh (11) M c so that the total moment release is M 0=M Z max [M 0 ] max 0 = M 0 ( dn ) (12) M 0=0 M thresh r M1 M 2 + ln M max + 1 M 1 ln M ln 1 + M thresh : M thresh M c When applying (10) to the transition zone population, we note that the populations of deep events are significantly different in the Tonga Fiji area and in the rest of the world (Giardini, 1984; Frohlich, 1989). Based on the results of Okal and Kirby (1995) for the depth range km, adequate constants would be M thresh = dyn-cm worldwide; M 1 = dyn-cm, M 2 = 6: dyn-cm in Tonga Fiji; and

16 Log 10 M 2 (dyn-cm) Log 10 M 1 (dyn-cm) Figure 3. Contoured value of the maximum rate of seismic moment release in the deep mantle, as a function of the corner moments M 1 and h R max 0 M 2 in (1). The function contoured is log 10 M i. Thus, for the reference period (M thresh thresh = dyn-cm; = 19 yr), R is found to vary between 5: and 1: dyn-cm/yr. M 1 = 1: dyn-cm, M dyn-cm outside Fiji (a value much smaller than would probably result in an excessively small width of less than 1 km for the seismogenic zone; thus we will use the upper bound M 2 = dyn-cm outside Fiji). The total CMT moment release beyond M thresh for the transition zone, 4: dyn-cm outside Fiji and 0: dyncm in Fiji, leads to z = 26:67 for Fiji and z = 26:78 outside Fiji. Obviously, it is very difficult, if not impossible, to propose adequate values of M c, both for the transition zone, and a fortiori, for the deep mantle. We make the simplifying assumption that the critical moments M c are comparable in the transition zone and the deep mantle. Assuming in turn that the stress drops involved would be of the same order (estimates of stress drops for deep earthquakes vary widely, and obviously we can only speculate as to their possible values in the lower mantle), this amounts to saying that the characteristic lengths c controlling the distribution would be comparable in both regions. In the case of transition zone earthquakes, it is possible to find a maximum value of M c basedonthe observation that the dataset does not exhibit curvature in its frequency-moment relationship for M 0 M thresh. As detailed in Aki (1987) and Rundle (1993), the Fermi-Dirac distribution for shallow earthquakes with M c = 1: dyn-cm becomes significantly distinct from its asymptotic Gutenberg-Richter form around M 0 = 3: dyn-cm, i.e., when the first term neglected in the Taylor expansion of the logarithm in Rundle s (1993) Equation (26) becomes 1% of

17 81 the leading term. Since the distribution of transition zone earthquakes does not depart from Gutenberg- Richter behavior for M dyn-cm, we infer M c dyn-cm for that population. On the other hand, a minimum value of M c remains a matter of speculation. We use here a value of dyn-cm, which is several orders of magnitude below the smallest earthquakes studied at the surface of the Earth. At any rate, an even smaller value of M c would not significantly change the results which follow. Using adequate values of the constants z, wehave tabulated solutions of (10) as a function of M c, both for events in the transition zone, and for the possible seismicity of the lower mantle. After adding the contribution beyond M thresh, and in terms of the rate of seismic release R0 max, we find that the extrapolated estimate is increased to between 2.5 and 3: dyn-cm/yr, while the estimated range would vary between and 1: dyn-cm/yr, depending on the choice of the constants M c ;M 1 and M 2. On the other hand, in the transition zone, the contribution of M 0 <M thresh would bring the total seismic release rate to anywhere between 2:6 and3: dyn-cm/yr, depending on M c. Therefore, the maximum seismic moment release rate in the lower mantle (which would still be compatible with fewer than 1 earthquake above M thresh during the reference period), can be expressed as follows, relative to the rate in the transition zone during the same period: extrapolated estimate, about 1000 times less seismic; range of estimates, from 230 to 5100 times less seismic. Discussion and Conclusion Since there are no documented earthquakes in the lower mantle, we have had to employ several assumptions to obtain estimates of the maximum rate of seismic moment release, and we need to discuss their robustness in view of the resulting uncertainties. 1. We have assumed in our computations that the threshold moment M thresh fell below the first critical moment M 2 in (1). If on the other hand, the detection threshold takes place in the intermediate regime ( = 1=2), Equation (5) should be replaced by: Rthresh max < M r thresh M1 M thresh 1 + ln M max M 1 1 : (13) In practice, and for all values of M 1 between M thresh and M max, the values of Rthresh max are changed insignificantly (to between 5: and 1: dyn-cm). Finally, should M thresh fall in the high-moment field with = 1, i.e., above the larger critical moment M 1, the rate Rthresh max would be simply expressed by putting M 1 = M thresh in (10) and M 1 = M 2 = M thresh in (5). As for the contribution of the smaller moments below the detection threshold to the maximum moment release rate, we can make the simple argument that inserting a range with = 1=2 anywhere below M thresh, while keeping N (M thresh ) < 1, would result in a decrease of the number of earthquakes in that range (and consequently of the total seismic moment release), as comparedto the case without a = 1=2 regime, the latter being covered in the previous analysis, by just putting M 1 = M 2 in (12). Thus, we conclude that the assumption M thresh < M 2 could only have overestimated the seismic release in the lower mantle. 2. Also, in estimating the contribution of very small earthquakes to the total seismic release (10), we have assumed a common value of M c in the transition zone and in the lower mantle. In principle, the relative rates of seismic release could be affected by a disparity between M c values in the two regions; however, we found that R0 max for the lower mantle would be increased at most by a factor of 1.5, relative to its counterpart in the transition zone, in the case of two independent values of M c varying freely in the interval chosen above (10 15 to dyn-cm). 3. A final question to be addressed is that of the influence of having used a rather short reference time window the 19 years from 1977 to 1995,which is presently the only period during which a homogeneous catalog is available. From the catalog of Huang et al. (1997), covering the WWSSN era ( ), it is suggested that the average rate of deep seismic moment release was indeed comparable during those years, with a total release of 4: dyn-cm, this figure being complete down to dyn-cm, rather than for the CMT era. Note however, that this similarity is nearly exclusively the result of two gigantic earthquakes: the Colombian event during the WWSSN years and the Bolivian one during the CMT era. Since world-wide detection capabilities have not changed significantly between 1964 (when the WWSSN was completed) and 1977, it is probably safe to interpret the observed aseismicity of the lower man-

18 82 tle during as indicating that no earthquake with M dyn-cm took place during that period. The maximum rates Rthresh max (5), and consequently the estimates for R0 max, can thus be adjusted by a factor 19/32, the extrapolated estimate falling to between 1:5 and 2: dyn-cm/yr, while the range of estimates would be 4: to 6: dyn-cm/yr. It is not possible to extend this analysis further back in time, since detection capabilities changed drastically in the early 1960s. By comparing with the long-term rate of activity in the transition zone, we conclude that the lower mantle is at least 400 to 8000 times (with an extrapolated estimate of at least 1700 times) less seismic than the transition zone. These numbers can then be compared to the variation in seismic activity with depth above 690 km. Figure 4 compares schematically the values of total seismic moment release during the CMT era for three depth bins: the uppermost 70 km corresponding roughly to shallow earthquakes, the upper mantle from 70 to 400 km, the transition zone between 400 and 690 km. Once again, these estimates are based on the CMT dataset, which suffers from its short time span. However, it clearly underestimates both shallow and deep events (the largest CMT solution to date, the 1977 Indonesian earthquake, is about 100 times smaller than the biggest event ever detected the 1960 Chilean earthquake). In round numbers, the upper mantle is found to be about 7 times less seismic than the band of shallow earthquakes; seismicity in the transition zone drops by another factor of 3. However, the transition to the lower mantle is clearly different, since it involves at least 3 orders of magnitude less seismic activity. Thus, any lower mantle seismic release must be limited to very low levels, even when detection limits are factored in. At least some subducting slabs appear to penetrate into the lower mantle, and, while a subset of proposed failure mechanisms cannot operate in the pv + mw field, we know of no reason why all potential mechanisms for seismic stress release suddenly should cease to operate below 690 km depth. We suggest, therefore, that an absence of significant accumulated strain energy below this depth is responsible for the observed low seismic potential of the lower mantle. Both the absence of major phase transitions, with attendant buoyancy anomalies for generating deviatoric stresses, at greater depths and the inability of a fine-grained, weak, superplastic pv + mw zone to accumulate significant strain energy at greater depths are consistent with this interpretation. Appendix We present here individual discussions of the relocation of all events given a NEIC location deeper than 690 km, and posterior to Stark and Frohlich s (1985) study, and of those historical events whose depths Rees and Okal (1987) were unable to constrain. Post-1980 events: h NEIC > 690 km 12 April 1984; Original location: 24:124 S; 179:004 E; 694 km; m b = 4:6 The NEIC location results in an unacceptable residual at Nadi ( 16.6 s). The dataset of 10 P times converges on 23:95 S, 179:49 E, at a depth of 561 km, with no residuals exceeding 1.7 s. This solution is equivalent to the ISC s. 10 January 1985; Original location: 18:039 S; 178:501 W; 701 km The NEIC location is incompatible with the arrival times at the stations in Fiji and results in a standard deviation of 3.49 s. The dataset of 23 arrival times converges on 18:10 S, 178:13 W at 646 km ( = 0:92 s), in excellent agreement with the ISC location. 22 October 1985, 19:14 GMT; Original location: 20:158 S; 179:163 W; 700 km; m b = 5:5 The ISC location is given a depth of km. The Harvard CMT solution is at 684 km. The dataset of 32 arrival times converges on 685 km, but the depth resolution is weak. A Monte Carlo test injecting noise with G of just 1 s scatters the hypocentral depths from 664 to 700 km. The combination of our relocation, the ISC solution and the CMT depth suggest that this event is probably at the very bottom of the subduction zone 685 km 10 km). There is no reason to favor a deeper source, such as the NEIC depth. 22 October 1985, 19:29 GMT. Original location: 20:123 S; 179:309 W; 707 km This aftershock of the previous event is also given at 707 km by the ISC. The dataset of 17 arrival times converges on 710 km ( = 0:47 s), but there is little depth resolution with Monte Carlo relocations ( G = 1s) ranging in depth from 686 to 733 km. We prefer hold-

19 83 Figure 4. Comparison of the rates of seismic moment release for various depth ranges. The first three bars at the left were derived from the Harvard CMT file ( ); the fourth one illustrates the maximum possible level of activity of the lower mantle, as derived in our study, and relative to the activity in the transition zone. The bar is drawn at the extrapolated estimate (1700 times less seismic than the lower mantle), and the arrows show the range of estimates (400 to 8000 times less seismic). Absolute vertical scale arbitrary. ing the depth at 690 km, which results in a perfectly acceptable solution ( = 0:76 s). 09 May 1989; Original location: 17:694 S; 179:091 W; 692 km This event, labeled poor solution by the NEIC, is given at 693 km by the ISC but with very poor depth resolution (43 km). Our solution converges on 685 km, the standard deviation being only 0.01 s smaller than at 693 km, and the hypocenters from the Monte Carlo runs ( G = 1 s) are scattered from 631 to 735 km. There is no reason to believe that the earthquake is anomalously deep. 08 November 1989; Original location: 19:695 S; 178:749 W; 707 km This small event is listed at km by the ISC. Our relocation converges on 709 km ( = 0:27 s), but a solution at a constrained depth of 690 km is also excellent ( = 0:65 s). The Monte Carlo runs ( G = 1 s) yield depths ranging from 678 to 733 km. 19 May 1992; Original location: 21:974 S; 178:558 W; 696 km This event is located by the ISC at a much shallower location (282 km), with a precision (17 km) which clearly indicates that the PDE estimate was erroneous. This intermediate depth is also confirmed (280 km) by our relocation. 29 December 1992; Original location: 20:33 S; 178:95 W; 695 km This relatively small event (m b = 4:4) is listed at km by the ISC. Our relocation converges on a similar value of 664 km when station MBL is eliminated (its residual with respect to the final location is 17.6 s). However, depth resolution is poor, as indicated both by the ISC error bar and by the range of Monte Carlo hypocenters (620 to 729 km). Historical events; h NEIC 670 km 25 August 1933; Original location: 6 S; 121 E; 720 km; M = 6:5 (G R) Note that the ISS lists this event as shallow.we were unable to find any readable records of this earthquake, which took place 90 mn after a much stronger event in Sichuan (M PAS = 7:4). The times at the closest station, Amboina, are generally incompatible with the remainder of the data, but increasing them by one minute leads to a satisfactory solution at 6:1 S; 120:8 E, h = 607 km with = 2:56 s on 9 stations. However, the dataset has no depth resolution, with Monte Carlo hypocenters ( G = 4 s) ranging from 160 to 751 km depth. The earthquake is probably deep, but there is no reason to give it an anomalously deep focus.